1. Field of the Invention
The present invention relates to a method for selecting a photomask substrate, and more particularly, it relates to a method for selecting a photomask substrate for use in a photolithography process which uses a polarized light as an illumination light, a method for manufacturing a photomask, and a method for manufacturing a semiconductor device.
2. Description of the Related Art
In recent years, a polarized light has been used as an illumination light in a photolithography process to form a very small element pattern on a semiconductor substrate (e.g., Japanese Patent No. 3246615). The “polarized light” is a light in which a vibration direction of an electric vector is aligned in a specific direction. When an illumination light is brought into a polarized light of a proper state in the photolithography process, the element pattern on a photomask is transferred to the semiconductor substrate with desired accuracy, whereby an element pattern of a shape smaller than a wavelength of the illumination light can be formed on the semiconductor substrate. The “state of polarized light” is a direction of a polarized direction, i.e., a vibration light of an electric vector.
However, when the polarized light passes through a birefringence material having birefringence, a polarizing direction of the polarized light rotates to change the state of the polarized light. The “birefringence” is a phenomenon in which the polarized light passing through the birefringence material is divided into a plurality of polarized lights of different speeds dependent on the vibration direction of the electric vector. A speed difference generated in the polarized lights advancing through the birefringence material is observed as a phase difference between the polarized lights which have passed through the birefringence material. Generally, a polarize state of the polarized light passing through the birefringence material fluctuates.
Thus, if the photomask is made of a birefringence material, when a polarized state of an illumination light passing through the photomask fluctuates, contrast of an image projected on the semiconductor substrate also fluctuates. In other words, in the photolithography process in which the photomask is made of a birefringence material and the polarized light is used as the illumination light, depending on a fluctuation amount of the polarized state of the illumination light, a shape of a photoresist film formed on the semiconductor substrate deviates from a desired shape. Hereinafter, deviation from the desired shape will be referred to as “shape fluctuation”. The shape fluctuation is a two-dimensional fluctuation with respect to a desired pattern width of the photoresist film, not including a thickness fluctuation.
A size of the fluctuation amount of the polarized state of the illumination light depends on a size of birefringence of the photomask through which the illumination light passes. The “size of the birefringence” is a speed difference generated when the polarized lights pass through the birefringence material, and observed as a phase difference between the polarized lights. For example, the size of the birefringence is represented as a phase difference between two polarized lights which pass through the birefringence material by 1 cm. Generally, the phase difference is represented by a wavelength of the polarized light. For example, in the case of an argon fluoride (ArF) excimer laser beam whose center wavelength is 193 nm, a phase difference of one wavelength is 193 nm. Accordingly, [nm/cm] is used for a size unit of the birefringence.
The size of the fluctuation amount of the polarized state of the illumination light depends on the size of the birefringence of the photomask. Accordingly, in-plane variance of the size of the birefringence of the photomask causes in-plane variance of a fluctuation amount of the shape of the photoresist film formed on the semiconductor substrate. In other words, the in-plane variance of the size of the birefringence of the photomask causes size variance of the element pattern transferred to the semiconductor substrate. Consequently, when there is the birefringence in the photomask, an image of a desired shape may not be transferred to the semiconductor substrate.
Generally, a fluctuation amount (hereinafter referred to as “polarization error sensitivity”) of the shape of the element pattern transferred to the semiconductor substrate with respect to a fluctuation amount of the polarized state of the illumination light is larger as an element pattern to be transferred is smaller. Accordingly, to form a very small element pattern on the semiconductor substrate, a photomask of small birefringence must be applied to the photolithography process. For example, a size of birefringence is set to 1 nm or less per photomask thickness.
A size of birefringence of the photomask is known to reflect a distribution of heat applied to a photomask substrate during its manufacturing process. Thus, for example, by executing annealing, improving a cooling method of the photomask substrate, adjusting a composition of the photomask substrate or the like in the manufacturing process of the photomask substrate, in-plane variance of a size of birefringence of the photomask substrate is reduced (e.g., Jpn. Pat. Appln. KOKAI Publication No. 2000-330263). A mask substrate of small in-plane variance of a size of birefringence is selected from a plurality of manufactured photomask substrates, and an element pattern is formed on the selected photomask substrate to manufacture a photomask.
However, the manufacturing of the photomask substrate small in-plane variance of a size of birefringence needs a high level technology, and it is difficult to increase yield of photomask substrates small in-plane variance of a size of birefringence. In consequence, photomask substrate manufacturing costs are increased, causing an increase in photomask manufacturing costs. In short, there is a problem of an increase in semiconductor device manufacturing costs.